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Register a new userJoint embedding of structure and features via graph convolutional networks
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The creation of social ties is largely determined by the entangled effects of peoples similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of the emergent network structure. We propose emph{AN2VEC}, a node embedding method which ultimately aims at disentangling the information shared by the structure of a network and the features of its nodes. Building on the recent developments of Graph Convolutional Networks (GCN), we develop a multitask GCN Variational Autoencoder where different dimensions of the generated embeddings can be dedicated to encoding feature information, network structure, and shared feature-network information. We explore the interaction between these disentangled characters by comparing the embedding reconstruction performance to a baseline case where no shared information is extracted. We use synthetic datasets with different levels of interdependency between feature and network characters and show (i) that shallow embeddings relying on shared information perform better than the corresponding reference with unshared information, (ii) that this performance gap increases with the correlation between network and feature structure, and (iii) that our embedding is able to capture joint information of structure and features. Our method can be relevant for the analysis and prediction of any featured network structure ranging from online social systems to network medicine.
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Recent studies on Graph Convolutional Networks (GCNs) reveal that the initial node representations (i.e., the node representations before the first-time graph convolution) largely affect the final model performance. However, when learning the initial representation for a node, most existing work linearly combines the embeddings of node features, without considering the interactions among the features (or feature embeddings). We argue that when the node features are categorical, e.g., in many real-world applications like user profiling and recommender system, feature interactions usually carry important signals for predictive analytics. Ignoring them will result in suboptimal initial node representation and thus weaken the effectiveness of the follow-up graph convolution. In this paper, we propose a new GCN model named CatGCN, which is tailored for graph learning when the node features are categorical. Specifically, we integrate two ways of explicit interaction modeling into the learning of initial node representation, i.e., local interaction modeling on each pair of node features and global interaction modeling on an artificial feature graph. We then refine the enhanced initial node representations with the neighborhood aggregation-based graph convolution. We train CatGCN in an end-to-end fashion and demonstrate it on semi-supervised node classification. Extensive experiments on three tasks of user profiling (the prediction of user age, city, and purchase level) from Tencent and Alibaba datasets validate the effectiveness of CatGCN, especially the positive effect of performing feature interaction modeling before graph convolution.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the alignment of geometric node embeddings of graphs, yield state-of-the-art performance. However, these graph kernels are not necessarily positive-definite. More importantly, computing the graph kernel matrix will have at least quadratic {time} complexity in terms of the number and the size of the graphs. In this paper, we propose a new family of global alignment graph kernels, which take into account the global properties of graphs by using geometric node embeddings and an associated node transportation based on earth movers distance. Compared to existing global kernels, the proposed kernel is positive-definite. Our graph kernel is obtained by defining a distribution over emph{random graphs}, which can naturally yield random feature approximations. The random feature approximations lead to our graph embeddings, which is named as random graph embeddings (RGE). In particular, RGE is shown to achieve emph{(quasi-)linear scalability} with respect to the number and the size of the graphs. The experimental results on nine benchmark datasets demonstrate that RGE outperforms or matches twelve state-of-the-art graph classification algorithms.
Graph convolution operator of the GCN model is originally motivated from a localized first-order approximation of spectral graph convolutions. This work stands on a different view; establishing a textit{mathematical connection between graph convolution and graph-regularized PCA} (GPCA). Based on this connection, GCN architecture, shaped by stacking graph convolution layers, shares a close relationship with stacking GPCA. We empirically demonstrate that the textit{unsupervised} embeddings by GPCA paired with a 1- or 2-layer MLP achieves similar or even better performance than GCN on semi-supervised node classification tasks across five datasets including Open Graph Benchmark footnote{url{https://ogb.stanford.edu/}}. This suggests that the prowess of GCN is driven by graph based regularization. In addition, we extend GPCA to the (semi-)supervised setting and show that it is equivalent to GPCA on a graph extended with ghost edges between nodes of the same label. Finally, we capitalize on the discovered relationship to design an effective initialization strategy based on stacking GPCA, enabling GCN to converge faster and achieve robust performance at large number of layers. Notably, the proposed initialization is general-purpose and applies to other GNNs.
Graph Neural Networks (GNNs) achieve an impressive performance on structured graphs by recursively updating the representation vector of each node based on its neighbors, during which parameterized transformation matrices should be learned for the node feature updating. However, existing propagation schemes are far from being optimal since they do not fully utilize the relational information between nodes. We propose the information maximizing graph neural networks (IGNN), which maximizes the mutual information between edge states and transform parameters. We reformulate the mutual information as a differentiable objective via a variational approach. We compare our model against several recent variants of GNNs and show that our model achieves the state-of-the-art performance on multiple tasks including quantum chemistry regression on QM9 dataset, generalization capability from QM9 to larger molecular graphs, and prediction of molecular bioactivities relevant for drug discovery. The IGNN model is based on an elegant and fundamental idea in information theory as explained in the main text, and it could be easily generalized beyond the contexts of molecular graphs considered in this work. To encourage more future work in this area, all datasets and codes used in this paper will be released for public access.
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